Necropolis – “Dawn from All Sides” [Campaign 2, Mission 3]

Or is the army reduction in the dungeon due to lag?

No, it's not lag. Inferno has a building in its castle that requires the Tear of Ashi (Wrath of Urgash). This building allows you to cast Meteor Shower on an enemy hero each turn.

I completed the mission. First, I destroyed the Demons, then the Stronghold, and finally attacked the Necromancer castle, which is located near Miranda's castle. I gathered my troops and attacked Miranda. There were no difficulties in the mission.